Scotland Yard has refused to name the 64-year-old, but Gambaccini's identity was confirmed by sources on Friday.
The DJ becomes the 15th arrest under Operation Yewtree since it began a year ago.
He was arrested under the "others" strand of the investigation, meaning the allegations are not directly linked to Savile. He was held at an address in south London before being taken into police custody.
Paul has been released on bail, but has a date in early January to further pursue the matter.
New York-born Gambaccini, who has adopted the nickname "Professor of Pop" because of his breadth of knowledge of the genre, began his four-decade BBC career at Radio 1 in October 1973. He is the only person to have been a regular presenter on Radios 1, 2, 3 and 4, and he also had stints on breakfast television shows TV-am and GMTV.
His ruby anniversary was celebrated with a four-part BBC Radio 4 series, The Gambaccini Years, broadcast in August, featuring interviews with music luminaries like Elton and Tim Rice.
Four individuals have been charged under Operation Yewtree, including the Australian entertainer Rolf Harris, and celebrity publicist Max Clifford.
Meanwhile, the Crown Prosecution Service is considering whether to bring charges against Gary Glitter after receiving a full file of evidence against him earlier this month.
A CPS spokeswoman said: "We are not prepared to discuss the identities of those involved or the alleged offences in any greater detail before a charging decision has been reached. We are unable to give any timescale for charging decisions, except to say that all cases passed to us for a charging decision will be considered very carefully and thoroughly, and decisions will be made as soon as is practicable."